Here are the facts:
1 lb. of fat = 3500 calories
Bicycling, stationary, moderate effort is approximately 500 calories / hour, vigorous effort is approximately 800 calories / hour.
So, if you cycle moderately for 1/2 hour per day, you will have to burn off 28 x 3500 calories = 98000 calories which will take you approximately 392 days, assuming you don't eat more to compensate for the increased metabolism. At a vigorous rate, 245 days.
If you are happy with this, then 1/2 hour is enough. If you would like a faster rate of improvement, go a little heavier and/or longer exercising or combine with some weight training or ease back on your calorie intake or, preferably, all of the above.